A174830 Odd numbers k such that k^2 is an abundant number.

105, 315, 495, 525, 585, 735, 945, 1155, 1365, 1485, 1575, 1755, 1785, 1995, 2145, 2205, 2415, 2475, 2625, 2805, 2835, 2925, 3045, 3135, 3255, 3315, 3465, 3675, 3705, 3795, 3885, 4095, 4305, 4455, 4485, 4515, 4725, 4785, 4845, 4935, 5115, 5145, 5265

Offset

1,1

Comments

Submitted at the suggestion of T. D. Noe.

For any number k, the abundance of k^2 is an odd number.

From Amiram Eldar, Jan 16 2025: (Start)

The least term that is not divisible by 5 is a(75) = 9009.

The least term that is not divisible by 3 is a(296889) = 37182145.

The least term that is coprime to 15 is 3909612711980232366109. (End)

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Formula

a(n) = sqrt(A156942(n)). - M. F. Hasler, Jan 26 2020

Mathematica

fQ[n_] := Block[{ds = DivisorSigma[1, n^2] - 2 n^2}, ds > 0 && OddQ@ ds]; Select[ Range[1, 5353, 2], fQ@# &]

Prog

(PARI) is(n)=n%2 && sigma(n^2, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017
(PARI) [2*k-1|k<-[1..6e3\2], sigma((2*k-1)^2, -1)>2] \\ M. F. Hasler, Jan 26 2020

Crossrefs

Cf. A005101, A005231, A033880, A156942.

Sequence in context: A046299 A010090 A306122 * A325312 A147576 A145752

Adjacent sequences: A174827 A174828 A174829 * A174831 A174832 A174833

Keyword

nonn

Author

Robert G. Wilson v, Mar 30 2010

Extensions

Name corrected by T. D. Noe, Jul 09 2010

Status

approved